We study gravitational waves from a hierarchical three-body system up to first-order post-Newtonian approximation. Under certain conditions, the existence of a nearby third body can cause periodic exchange between eccentricity of an inner binary and relative inclination, known as Kozai-Lidov oscillations. We analyze features of the waveform from the inner binary system undergoing such oscillations. We find that variation caused due to the tertiary companion can be observed in the gravitational waveforms and energy spectra, which should be compared with those from isolated binaries and coplanar three-body system. The detections from future space-based interferometers will make possible the investigation of gravitational wave spectrum in mHz range and may fetch signals by sources addressed.

Abstract

We analyze the collisional Penrose process between a particle on the innermost stable circular orbit (ISCO) orbit around an extreme Kerr black hole and a particle impinging from infinity. We consider both cases with non-spinning and spinning particles. We evaluate the maximal efficiency, $\eta_{\text{max } }=(\text{extracted energy})/(\text{input energy})$, for the elastic collision of two massive particles and for the photoemission process, in which the ISCO particle will escape to infinity after a collision with a massless impinging particle. For non-spinning particles, the maximum efficiency is $\eta_{\text{max } } \approx 2.562$ for the elastic collision and $\eta_{\text{max } } \approx 7$ for the photoemission process. For spinning particles we obtain the maximal efficiency $\eta_{\text{max } } \approx 8.442$ for the elastic collision and $\eta_{\text{max } } \approx 12.54$ for the photoemission process.

We study a hierarchical triple system with the Kozai–Lidov mechanism, and analyse the cumulative shift of periastron time of a binary pulsar by the emission of gravitational waves. Time evolution of the osculating orbital elements of the triple system is calculated by directly integrating the first-order post-Newtonian equations of motion. The Kozai–Lidov mechanism will bend the evolution curve of the cumulative shift when the eccentricity becomes large. We also investigate the parameter range of mass and semimajor axis of the third companion with which the bending of the cumulative-shift curve could occur within 100 yr.

© 2018 American Physical Society. We analyze the collisional Penrose process of spinning test particles in an extreme Kerr black hole. We consider that two particles plunge into the black hole from infinity and collide near the black hole. For the collision of two massive particles, if the spins of particles are s1≈0.01379 μM and s2≈-0.2709 μM, we obtain the maximal efficiency is about ηmax=(extracted energy)/(input energy)≈15.01, which is more than twice as large as the case of the collision of non-spinning particles (ηmax≈6.32). We also evaluate the collision of a massless particle without spin and a massive particle with spin (Compton scattering), in which we find the maximal efficiency is ηmax≈26.85 when s2≈-0.2709 μM, which should be compared with ηmax≈13.93 for the nonspinning case.

We propose a hybrid type of the conventional Higgs inflation and new Higgs inflation models. We perform a disformal transformation into the Einstein frame and analyze the background dynamics and the cosmological perturbations in the truncated model, in which we ignore the higher-derivative terms of the Higgs field. From the observed power spectrum of the density perturbations, we obtain the constraint on the nonminimal coupling constant ξ and the mass parameter M in the derivative coupling. Although the primordial tilt ns in the hybrid model barely changes, the tensor-to-scalar ratio r moves from the value in the new Higgs inflationary model to that in the conventional Higgs inflationary model as |ξ| increases. We confirm our results by numerical analysis by ADM formalism of the full theory in the Jordan frame.

We find vacuum solutions such that massive gravitons are confined in a local spacetime region by their gravitational energy in asymptotically flat spacetimes in the context of the bigravity theory. We call such self-gravitating objects massive graviton geons. The basic equations can be reduced to the Schrödinger-Poisson equations with the tensor "wave function" in the Newtonian limit. We obtain a nonspherically symmetric solution with j=2, =0 as well as a spherically symmetric solution with j=0, =2 in this system where j is the total angular momentum quantum number and is the orbital angular momentum quantum number, respectively. The energy eigenvalue of the Schrödinger equation in the nonspherical solution is smaller than that in the spherical solution. We then study the perturbative stability of the spherical solution and find that there is an unstable mode in the quadrupole mode perturbations which may be interpreted as the transition mode to the nonspherical solution. The results suggest that the nonspherically symmetric solution is the ground state of the massive graviton geon. The massive graviton geons may decay in time due to emissions of gravitational waves but this timescale can be quite long when the massive gravitons are nonrelativistic and then the geons can be long-lived. We also argue possible prospects of the massive graviton geons: applications to the ultralight dark matter scenario, nonlinear (in)stability of the Minkowski spacetime, and a quantum transition of the spacetime.

We study coherently oscillating massive gravitons in the ghost-free bigravity theory. This coherent field can be interpreted as a condensate of the massive gravitons. We first define the effective energy-momentum tensor of the coherent massive gravitons in a curved spacetime. We then study the background dynamics of the Universe and the cosmic structure formation including the effects of the coherent massive gravitons. We find that the condensate of the massive graviton behaves as a dark matter component of the Universe. From the geometrical point of view the condensate is regarded as a spacetime anisotropy. Hence, in our scenario, dark matter is originated from the tiny deformation of the spacetime. We also discuss a production of the spacetime anisotropy and find that the extragalactic magnetic field of a primordial origin can yield a sufficient amount for dark matter.

Energy extraction from a rotating or charged black hole is one of the fascinating issues in general relativity. The collisional Penrose process is one such extraction mechanism and has been reconsidered intensively since Bañados, Silk, and West pointed out the physical importance of very high energy collisions around a maximally rotating black hole. In order to get results analytically, the test particle approximation has been adopted so far. Successive works based on this approximation scheme have not yet revealed the upper bound on the efficiency of the energy extraction because of the lack of backreaction. In the Reissner-Nordström spacetime, by fully taking into account the self-gravity of the shells, we find that there is an upper bound on the extracted energy that is consistent with the area law of a black hole. We also show one particular scenario in which almost the maximum energy extraction is achieved even without the Bañados-Silk-West collision.

We study the cosmological dynamics of a D-BIonic and Dirac-Born-Infeld scalar field, which is coupled to matter fluid. For the exponential potential and the exponential couplings, we find a new analytic scaling solution yielding the accelerated expansion of the Universe. Since it is shown to be an attractor for some range of the coupling parameters, the density parameter of matter fluid can be the observed value, as in the coupled quintessence with a canonical scalar field. Contrary to the usual coupled quintessence, where the value of the matter coupling giving the observed density parameter is too large to satisfy the observational constraint from the cosmic microwave background, we show that the D-BIonic theory can give a similar solution with a much smaller value of matter coupling. As a result, together with the fact that the D-BIonic theory has a screening mechanism, the D-BIonic theory can solve the so-called coincidence problem as well as the dark energy problem.

We study the Einstein-SO(3) Yang-Mills-Higgs system with a negative cosmological constant and find the monopole black hole solutions as well as the trivial Reissner-Nordstrm black hole. We discuss thermodynamical stability of the monopole black hole in an isolated system. We expect a phase transition between those two black holes when the mass of a black hole increases or decreases. The type of phase transition depends on the cosmological constant Lambda, as well as the vacuum expectation value upsilon and the coupling constant lambda of the Higgs field. Keeping lambda small, we find there are two critical values of the cosmological constant, Lambda(cr(1)) (upsilon) and Lambda(cr(2)) (upsilon), which depend on upsilon. If Lambda(cr(1)) (upsilon) < Lambda(< 0), we find the first order transition, whereas if Lambda(cr(2)) (upsilon) < Lambda < Lambda(cr(1)) (upsilon), the transition becomes second order. For the case of Lambda(b) (upsilon) < Lambda < Lambda((2)) (upsilon), we again find the first order irreversible transition from the monopole black hole to the extreme Reissner-Nordstrm black hole. Beyond Lambda(b) (upsilon), no monopole black hole exists. We also discuss thermodynamical properties of the monopole black hole in a thermal bath system.

The gravitational baryogensis may not generate a sufficient baryon asymmetry in the standard thermal history of the Universe when we take into account the gravitino problem. Hence, it has been suggested that anisotropy of the Universe can enhance the generation of the baryon asymmetry through the increase of the time change of the Ricci scalar curvature. We study the gravitational baryogenesis in the presence of anisotropy, which is produced at the end of an anisotropic inflation. Although we confirm that the generated baryon asymmetry is enhanced compared with the original isotropic cosmological model, taking into account the constraint on the anisotropy by the recent CMB observations, we find that it is still difficult to obtain the observed baryon asymmetry only through the gravitational baryogenesis without suffering from the gravitino problem.

© 2016 American Physical Society.The gravitational baryogensis may not generate a sufficient baryon asymmetry in the standard thermal history of the Universe when we take into account the gravitino problem. Hence, it has been suggested that anisotropy of the Universe can enhance the generation of the baryon asymmetry through the increase of the time change of the Ricci scalar curvature. We study the gravitational baryogenesis in the presence of anisotropy, which is produced at the end of an anisotropic inflation. Although we confirm that the generated baryon asymmetry is enhanced compared with the original isotropic cosmological model, taking into account the constraint on the anisotropy by the recent CMB observations, we find that it is still difficult to obtain the observed baryon asymmetry only through the gravitational baryogenesis without suffering from the gravitino problem.

Assuming static and spherically symmetric spacetimes in the ghost-free bigravity theory, we find a relativistic star solution, which is very close to that in general relativity. The coupling constants are classified into two classes: Class [I] and Class [II]. Although the Vainshtein screening mechanism is found in the weak gravitational field for both classes, we find that there is no regular solution beyond the critical value of the compactness in Class [I]. This implies that the maximum mass of a neutron star in Class [I] becomes much smaller than that in general relativity (GR). On the other hand, for the solution in Class [II], the Vainshtein screening mechanism works well even in a relativistic star and the result in GR is recovered.

© 2016 American Physical Society.Assuming static and spherically symmetric spacetimes in the ghost-free bigravity theory, we find a relativistic star solution, which is very close to that in general relativity. The coupling constants are classified into two classes: Class [I] and Class [II]. Although the Vainshtein screening mechanism is found in the weak gravitational field for both classes, we find that there is no regular solution beyond the critical value of the compactness in Class [I]. This implies that the maximum mass of a neutron star in Class [I] becomes much smaller than that in general relativity (GR). On the other hand, for the solution in Class [II], the Vainshtein screening mechanism works well even in a relativistic star and the result in GR is recovered.

We study a static, spherically symmetric and asymptotic flat spacetime, assuming the hypersurface orthogonal Einstein-aether theory with an ultraviolet modification motivated by the Hořava-Lifshitz theory, which is composed of the z=2 Lifshitz scaling terms such as scalar combinations of a three-Ricci curvature and the acceleration of the aether field. For the case with the quartic term of the acceleration of the aether field, we obtain a two-parameter family of black hole solutions, which possess a regular universal horizon. Whereas, if a three-Ricci curvature squared term is joined in ultraviolet modification, we find a solution with a thunderbolt singularity such that the universal horizon turns out to be a spacelike singularity.

We study a static, spherically symmetric and asymptotic flat spacetime, assuming the hypersurface orthogonal Einstein-aether theory with an ultraviolet modification motivated by the Horava-Lifshitz theory, which is composed of the z = 2 Lifshitz scaling terms such as scalar combinations of a three-Ricci curvature and the acceleration of the aether field. For the case with the quartic term of the acceleration of the aether field, we obtain a two-parameter family of black hole solutions, which possess a regular universal horizon. Whereas, if a three-Ricci curvature squared term is joined in ultraviolet modification, we find a solution with a thunderbolt singularity such that the universal horizon turns out to be a spacelike singularity.

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lemaître-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-0 mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the Stückelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lemaitre-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-0 mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the Stuckelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

We argue a scenario motivated by the context of string landscape, where our Universe is produced by a new vacuum bubble embedded in an old bubble and these bubble universes have not only different cosmological constants, but also their own different gravitational constants. We study these effects on the primordial curvature perturbations. In order to construct a model of varying gravitational constants, we use the Jordan-Brans-Dicke theory where different expectation values of scalar fields produce difference of constants. In this system, we investigate the nucleation of the bubble universe and the dynamics of the wall separating two spacetimes. In particular, the primordial curvature perturbation on superhorizon scales can be affected by the wall trajectory as the boundary effect. We show how the gravitational constant in the exterior bubble universe modifies the power spectrum, that provides a peak like a bump feature at a large scale.

We study the origin of dark matter based on the ghost-free bigravity theory with twin matter fluids. The present cosmic acceleration can be explained by the existence of graviton mass, while dark matter is required in several cosmological situations (the galactic missing mass, the cosmic structure formation and the cosmic microwave background observation). Assuming that the Compton wavelength of the massive graviton is shorter than a galactic scale, we show the bigravity theory can explain dark matter by twin matter fluid as well as the cosmic acceleration by tuning appropriate coupling constants.

We study gravitational theories with a cosmological constant and the Gauss-Bonnet curvature squared term and analyze the possibility of de Sitter expanding spacetime with a constant internal space. We find that there are two branches of the de Sitter solutions: both the curvature of the internal space and the cosmological constant are (1) positive and (2) negative. From the stability analysis, we show that the de Sitter solution of the case (1) is unstable, while that in the case (2) is stable. Namely de Sitter solution in the present system is stable if the cosmological constant is negative. We extend our analysis to the gravitational theories with higher-order Lovelock curvature terms. Although the existence and the stability of the de Sitter solutions are very complicated and highly depend on the coupling constants, there exist stable de Sitter solutions similar to the case (2). We also find de Sitter solutions with Hubble scale much smaller than the scale of a cosmological constant, which may explain a discrepancy between an inflation energy scale and the Planck scale.

We study dynamics of Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime based on the ghost-free bigravity theory. Assuming the coupling parameters guaranteeing the existence of de Sitter space as well as Minkowski spacetime, we find two stable attractors for spacetime with "twin" dust matter fields: One is de Sitter accelerating universe and the other is matter dominated universe. Although a considerable number of initial data leads to de Sitter universe, we also find matter dominated universe or spacetime with a future singularity for some initial data. The cosmic no-hair conjecture does not exactly hold, but the accelerating expansion can be found naturally. The Lambda-CDM model is obtained as an attractor. We also show that the dark matter component in the Friedmann equation, which originates from another twin matter, can be about 5 times larger than the baryonic matter, by choosing the appropriate coupling constants.

We study anisotropic cosmologies of a scalar field interacting with an SU(2) gauge field via a gauge-kinetic coupling. We analyze Bianchi class A models, which include Bianchi type I, II, VI0, VII0, VIII and IX. The linear stability of isotropic inflationary solution with background magnetic field is shown, which generalizes the known results for U(1) gauge fields. We also study anisotropic inflationary solutions, all of which turn out to be unstable. Then nonlinear stability for the isotropic inflationary solution is examined by numerically investigating the dependence of the late-time behaviour on the initial conditions. We present a number of novel features that may well affect physical predictions and viability of the models. First, in the absence of spatial curvature, strong initial anisotropy leads to a rapid oscillation of gauge field, thwarting convergence to the inflationary attractor. Secondly, the inclusion of spatial curvature destabilizes the oscillatory attractor and the global stability of the isotropic inflation with gauge field is restored. Finally, based on the numerical evidence combined with the knowledge of the eigenvalues for various inflationary solutions, we give a generic lower-bound for the duration of transient anisotropic inflation, which is inversely proportional to the slow-roll parameter. © 2013 IOP Publishing Ltd and Sissa Medialab srl.

We study Bianchi cosmologies in the ghost-free bigravity theory, assuming both metrics to be homogeneous and anisotropic and of the Bianchi class A, which includes types I, II, VI0, VII0, VIII, and IX. We assume the Universe to contain a radiation and a nonrelativistic matter, with the cosmological term mimicked by the graviton mass. We find that, for generic initial values leading to a late-time self-acceleration, the Universe approaches a state with nonvanishing anisotropies. The anisotropy contribution to the total energy density decreases much slower than in General Relativity and shows the same falloff rate as the energy of a nonrelativistic matter. The solutions show a singularity in the past, and in the Bianchi IX case, the singularity is approached via a sequence of Kasner-like steps, which is characteristic of a chaotic behavior.

We study the dynamics of the homogeneous and isotropic universe with a scalar field and an SU(2) non-Abelian gauge (Yang-Mills) field. The scalar field has an exponential potential and the Yang-Mills field is coupled to the scalar field with an exponential function of the scalar field. We find that the magnetic component of the Yang-Mills field assists acceleration of the cosmic expansion and a power-law inflation becomes possible even if the scalar field potential is steep, which may be expected from some compactification of higher-dimensional unified theories of fundamental interactions. This power-law inflationary solution is a stable attractor in a certain range of coupling parameters. Unlike the case with multiple Abelian gauge fields, the power-law inflationary solution with the dominant electric component is unstable because of the existence of nonlinear coupling of the Yang-Mills field. We also analyze the dynamics for the noninflationary regime, and find several attractor solutions. © 2013 American Physical Society.

The stealth scalar field is a nontrivial configuration without any backreaction to geometry, which is characteristic for nonminimally coupled scalar fields. Studying the creation probability of the de Sitter universe with a stealth scalar field by Hartle and Hawking's semiclassical method, we show that the effect of the stealth field can be significant. For the class of scalar fields we consider, creation with a stealth field is possible for a discrete value of the coupling constant, and its creation probability is always less than that with a trivial scalar field. However, those creation rates can be almost the same depending on the parameters of the theory. DOI: 10.1103/PhysRevD.86.124045

We present the time-dependent solutions corresponding to the dynamical D-brane with angles in ten-dimensional type II supergravity theories. Our solutions with angles are different from the known dynamical intersecting brane solutions in supergravity theories. Because of our ansatz for fields, all warp factors in the solutions can depend on time. Applying these solutions, we construct cosmological models from those solutions by smearing some dimensions and compactifying the internal space. We find the Friedmann-Lemaitre-Robertson-Walker cosmological solutions with power-law expansion. We also discuss the dynamics of branes based on these solutions. When the spacetime is contracting in ten dimensions, each brane approaches the others as the time evolves. However, for a Dp-brane (p <= 7) without smearing branes, a singularity appears before branes collide. In contrast, the D6-D8-brane system or the smeared D(p - 2) - Dp-brane system with one uncompactified extra dimension can provide an example of colliding branes (and collision of the universes), if they have the same charges.

We study cosmological solutions in the effective heterotic string theory with a alpha'-correction terms in the string frame. It is pointed out that the effective theory has an ambiguity via field redefinition and we analyze generalized effective theories due to this ambiguity. We restrict our analysis to the effective theories which give equations of motion of second order in the derivatives, just as "Galileon" field theory. This class of effective actions contains two free coupling constants. We find de Sitter solutions as well as the power-law expanding universes in our four-dimensional Einstein frame. The accelerated expanding universes are always attractors in the present dynamical system.

We study a vacuum Bianchi IX universe in the context of Horava-Lifshitz gravity. In particular, we focus on the classical dynamics of the universe and analyze how anisotropy changes the history of the universe. For small anisotropy, we find an oscillating universe as well as a bounce universe just as the case of the Friedmann-Lemaitre-Robertson-Walker spacetime. However, if the initial anisotropy is large, we find the universe which ends up with a big crunch after oscillations if a cosmological constant Lambda is zero or negative. For Lambda > 0, we find a variety of histories of the universe, that is a de Sitter expanding universe after oscillations in addition to the oscillating solution and the previous big crunch solution. This fate of the universe shows sensitive dependence of initial conditions, which is one of the typical properties of a chaotic system. If the initial anisotropy is near the upper bound, we find the universe starting from a big bang and ending up with a big crunch for Lambda <= 0, and a de Sitter expanding universe starting from a big bang for Lambda > 0.

We investigate the dynamics of a single spherical void embedded in a Friedmann-Lemaitre universe, and analyze the void shape in the redshift space. We find that the void in the redshift space appears as an ellipse shape elongated along the line of sight (i.e., an opposite deformation to the Kaiser effect). Applying this result to observed void candidates at the redshift z similar to 1-2, it may provide us with a new method to evaluate the cosmological parameters, in particular the value of a cosmological constant.

We find that anti-de Sitter (AdS) spacetime with a nontrivial linear dilaton field is an exact solution in the effective action of the string theory, which is described by gravity with the Gauss-Bonnet curvature terms coupled to a dilaton field in the string frame without a cosmological constant. The AdS radius is determined by the spacetime dimensions and the coupling constants of curvature corrections. We also construct the asymptotically AdS black hole solutions with a linear dilaton field numerically. We find these AdS black holes for hyperbolic topology and in dimensions higher than four. We discuss the thermodynamical properties of those solutions. Extending the model to the case with the even-order higher Lovelock curvature terms, we also find the exact AdS spacetime with a nontrivial dilaton. We further find a cosmological solution with a bounce of three-dimensional space and a solitonic solution with a nontrivial dilaton field, which is regular everywhere and approaches an asymptotically AdS spacetime.

Supersymmetric solutions of supergravity have been of particular importance in the advances of string theory. This article reviews the current status of black hole solutions in higher-dimensional supergravity theories. We discuss primarily the gravitational aspects of supersymmetric black holes and their relatives in various dimensions. Supersymmetric solutions and their systematic derivation are reviewed with prime examples. We also study the stationary or dynamically intersecting branes in ten and eleven-dimensions, which provide a number of interesting black objects via the dimensional reduction and duality transformations.

Starting with an aspect of motivation to study higher dimensional black holes, we give a brief overview of the whole volume. Finally we give a short note on notations and conventions.

In recent series of papers, we found an arbitrary dimensional, time-evolving, and spatially inhomogeneous solution in Einstein-Maxwell-dilaton gravity with particular couplings. Similar to the supersymmetric case, the solution can be arbitrarily superposed in spite of nontrivial time-dependence, since the metric is specified by a set of harmonic functions. When each harmonic has a single point source at the center, the solution describes a spherically symmetric black hole with regular Killing horizons and the spacetime approaches asymptotically to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology. We discuss in this paper that in 5 dimensions, this equilibrium condition traces back to the first-order "Killing spinor" equation in "fake supergravity" coupled to arbitrary U(1) gauge fields and scalars. We present a five-dimensional, asymptotically FLRW, rotating black-hole solution admitting a nontrivial "Killing spinor," which is a spinning generalization of our previous solution. We argue that the solution admits nondegenerate and rotating Killing horizons in contrast with the supersymmetric solutions. It is shown that the present pseudo-supersymmetric solution admits closed timelike curves around the central singularities. When only one harmonic is time-dependent, the solution oxidizes to 11 dimensions and realizes the dynamically intersecting M2/M2/M2-branes in a rotating Kasner universe. The Kaluza-Klein-type black holes are also discussed.

We study the dynamics of isotropic and homogeneous universes in the generalized Horava-Lifshitz gravity, and classify all possible evolutions of vacuum spacetime. In the case without the detailed balance condition, we find a variety of phase structures of vacuum spacetimes depending on the coupling constants as well as the spatial curvature K and a cosmological constant Lambda. A bounce universe solution is obtained for Lambda > 0, K = +/- 1 or Lambda = 0, K = -1, while an oscillation spacetime is found for Lambda >= 0, K = 1, or Lambda < 0, K = +/- 1. We also propose a quantum tunneling scenario from an oscillating spacetime to an inflationary universe, resulting in a macroscopic cyclic universe.

We present a class of dynamical solutions in a D-dimensional gravitational<br />
theory coupled to a dilaton, a form field strength, and a cosmological<br />
constant. We find that for any D due to the presence of a cosmological<br />
constant, the metric of solutions depends on a quadratic function of the brane<br />
world volume coordinates, and the transverse space cannot be Ricci flat except<br />
for the case of 1-branes. We then discuss the dynamics of 1-branes in a<br />
D-dimensional spacetime. For a positive cosmological constant, 1-brane<br />
solutions with D&gt;4 approach the Milne universe in the far-brane region. On the<br />
...

An exact solution representing black holes in an expanding universe is found. The black holes are maximally charged and the universe is expanding with arbitrary equation of state (P = w rho with -1 &lt;= for all w &lt;= 1). It is an exact solution of the Einstein-scalar-Maxwell system, in which we have two Maxwell-type U(1) fields coupled to the scalar field. The potential of the scalar field is an exponential. We find a regular horizon, which depends on one parameter [the ratio of the energy density of U(1) fields to that of the scalar field]. The horizon is static because of the balance on the horizon between gravitational attractive force and U(1) repulsive force acting on the scalar field. We also calculate the black hole temperature.

We construct a general family of supersymmetric solutions in time- and space-dependent wave backgrounds in general supergravity theories describing single and intersecting p-branes embedded into time-dependent dilaton-gravity plane waves of an arbitrary (isotropic) profile, with the brane world-volume aligned parallel to the propagation direction of the wave. We discuss how many degrees of freedom we have in the solutions. We also propose that these solutions can be used to describe higher-dimensional time-dependent "black holes", and discuss their property briefly.

We study physical properties and global structures of a time-dependent, spherically symmetric solution obtained via the dimensional reduction of intersecting M-branes. We find that the spacetime describes a maximally charged black hole which asymptotically tends to the Friedmann-Lemaitre-Robertson-Walker universe filled by a stiff matter. The metric solves the field equations of the Einstein-Maxwell-dilaton system, in which four Abelian gauge fields couple to the dilation with different coupling constants. The spacetime satisfies the dominant energy condition and is characterized by two parameters, Q and tau, related to the Maxwell charge and the relative ratio of black-hole horizon radii, respectively. In spite of the nontrivial time dependence of the metric, it turns out that the black-hole event horizon is a Killing horizon. This unexpected symmetry may be ascribed to the fact that the 11-dimensional brane configurations are supersymmetric in the static limit. Finally, combining with laws of the trapping horizon, we discuss the thermodynamic properties of the black hole. It is shown that the horizon possesses a nonvanishing temperature, contrary to the extremal Reissner-Nordstrom solution.

We present the black hole solutions and analyze their properties in the superstring effective field theory with the Gauss-Bonnet curvature correction terms. We find qualitative differences in our results from those obtained in the truncated model in the Einstein frame. The main difference in our model from the truncated one is that the existence of a turning point in the mass-area curve, the mass-entropy curve, and the mass-temperature curve in five and higher dimensions, where we expect a change of stability. We also find a mass gap in our model, where there is no black hole solution. In five dimensions, there exists a maximum black hole temperature and the temperature vanishes at the minimum mass, which is not found in the truncated model.

We present the black hole solutions and analyze their properties in the superstring effective field theory with the Gauss-Bonnet curvature correction terms. We find qualitative differences in our results from those obtained in the truncated model in the Einstein frame. The main difference in our model from the truncated one is that the existence of a turning point in the mass-area curve, the mass-entropy curve, and the mass-temperature curve in five and higher dimensions, where we expect a change of stability. We also find a mass gap in our model, where there is no black hole solution. In five dimensions, there exists a maximum black hole temperature and the temperature vanishes at the minimum mass, which is not found in the truncated model.

Minimal surfaces and domain walls play important roles in various contexts of spacetime physics as well as material science. In this paper, we first review the Bernstein conjecture, which asserts that a plane is the only globally well-defined solution of the minimal surface equation which is a single valued graph over a hyperplane in flat spaces, and its failure in higher dimensions. Then, we review how minimal cones in four- and higher-dimensional spacetimes, which are curved and even singular at the apex, may be used to provide counterexamples to the conjecture. The physical implications of these counterexamples in curved spacetimes are discussed from various points of view, ranging from classical general relativity, brane physics and holographic models of fundamental interactions.

A black hole casts a shadow as an optical appearance because of its strong gravitational field. We study how to determine the spin parameter and the inclination angle by observing the apparent shape of the shadow, which is distorted mainly by those two parameters. Defining some observables characterizing the apparent shape (its radius and distortion parameter), we find that the spin parameter and inclination angle of a Kerr black hole can be determined by the observation. This technique is also extended to the case of a Kerr naked singularity.

We present dynamical intersecting brane solutions in higher-dimensional gravitational theory coupled to dilaton and several forms. Assuming the forms of metric, form fields, and dilaton field, we give a complete classification of dynamical intersecting brane solutions with/without M-waves and Kaluza-Klein monopoles in eleven-dimensional super-gravity. We apply these solutions to cosmology and black holes. It is shown that these give FRW cosmological solutions and in some cases Lorentz invariance is broken in our world. If we regard the bulk space as our universe, we may interpret them as black holes in the expanding universe. We also discuss lower-dimensional effective theories and point out naive effective theories may give us some solutions which are inconsistent with the higher-dimensional Einstein equations.

We construct a fairy general family of supersymmetric solutions in time- and space-dependent backgrounds in general supergravity theories. One class of the solutions are intersecting brane solutions with factorized form of time- and space-dependent metrics, the second class are brane solutions in pp-wave backgrounds carrying spacetime-dependence, and the final class are the intersecting branes with more nontrivial spacetime-dependence, and their intersection rules are given. Physical properties of these solutions are discussed, and the relation to existing literature is also briefly mentioned. The number of remaining supersymmetries are identified for various configurations including single branes, D1-D5, D2-D6-branes with nontrivial dilaton, and their possible dual theories are briefly discussed.

In the scalar-tensor theory of gravitation it seems nontrivial to establish if solutions of the cosmological equations in the presence of a cosmological constant (or a vacuum energy) behave as attractors independently of the initial values. We develop a general formulation in terms of two-dimensional phase space, mainly according to the Brans-Dicke model requiring the scalar field decoupled from the matter Lagrangian in the Jordan frame. We show that there are two kinds of fixed points, one of which is an attractor depending on the coupling constant and equation of state. We find that the static universe in the Jordan frame is an attractor in the presence of a cosmological constant for some range of the coupling constant. We extend our analysis to a power-law potential, finding a new type of power-law inflation caused by the coupling to the matter fluid, also as an attractor.

We discuss the phase transitions between three states of a plasma fluid (plasma ball, uniform plasma tube, and non-uniform plasma tube), which are dual to the corresponding finite energy black objects (black hole, uniform black string, and non-uniform black string) localized in an asymptotically locally AdS space. Adopting the equation of state for the fluid obtained by the Scherk-Schwarz compactification of a conformal field theory, we obtain axisymmetric static equilibrium states of the plasma fluid and draw the phase diagrams with their thermodynamical quantities. By use of the fluid/gravity correspondence, we predict the phase diagrams of the AdS black holes and strings on the gravity side. The thermodynamic phase diagrams of the AdS black holes and strings show many similarities to those of the black hole-black string system in a Kaluza-Klein vacuum. For instance, the critical dimension for the smooth transition from the uniform to non-uniform strings is the same as that in the Kaluza-Klein vacuum in the canonical ensemble. The analysis in this paper may provide a holographic understanding of the relation between the Rayleigh-Plateau and Gregory-Laflamme instabilities via the fluid/gravity correspondence.

Although f(R) modified gravity models can be made to satisfy solar system and cosmological constraints, it has been shown that they have the serious drawback of the nonexistence of stars with strong gravitational fields. In this paper, we discuss whether or not higher curvature corrections can remedy the nonexistence consistently. The following problems are shown to arise as the costs one must pay for the f(R) models that allow for neutrons stars: (i) the leading correction must be fine-tuned to have the typical energy scale mu less than or similar to 10(-19) GeV, which essentially comes from the free fall time of a relativistic star; (ii) the leading correction must be further fine-tuned so that it is not given by the quadratic curvature term. The second problem is caused because there appears an intermediate curvature scale, and laboratory experiments of gravity will be under the influence of higher curvature corrections. Our analysis thus implies that it is a challenge to construct viable f(R) models without very careful and unnatural fine-tuning.

Based on the stochastic gravity, we study the loop corrections to the scalar and tensor perturbations during inflation. Since the loop corrections to scalar perturbations suffer infrared divergence, we consider the IR regularization to obtain the finite value. We find that the loop corrections to the scalar perturbations are amplified by the e-folding; in other words there appears the logarithmic correction, just as discussed by M. Sloth et al. On the other hand, we find that the tensor perturbations do not suffer from infrared divergence.

Several f(R) modified gravity models have been proposed which realize the correct cosmological evolution and satisfy solar system and laboratory tests. Although nonrelativistic stellar configurations can be constructed, we argue that relativistic stars cannot be present in such f(R) theories. This problem appears due to the dynamics of the effective scalar degree of freedom in the strong gravity regime. Our claim thus raises doubts on the viability of f(R) models.

Analyzing a capillary minimizing problem for a higher-dimensional extended fluid, we find that there exist startling similarities between the black hole-black string system (the Gregory-Laflamme instability) and the liquid drop-liquid bridge system (the Rayleigh-Plateau instability), which were first suggested by a perturbative approach. In the extended fluid system, we confirm the existence of the critical dimension above which the non-uniform bridge (NUB, i.e., Delaunay unduloid) serves as the global minimizer of surface area. We also find a variety of phase structures (one or two cusps in the volume-area phase diagram) near the critical dimension. Applying a catastrophe theory, we predict that in the 9-dimensional (9D) space and below, we have the first order transition from a uniform bridge (UB) to a spherical drop (SD), while in the 10D space and above, we expect the transition such that UB -&gt; NUB -&gt; SD. This gives an important indication for a transition in the black hole-black string system. (C) 2008 Elsevier B.V. All rights reserved.

We discuss the entropy-area relation for the small black holes with higher curvature corrections by using the entropy function formalism and field redefinition method. We show that the entropy S-BH of the small black hole is proportional to its horizon area A. In particular, we find a universal result that S-BH = A/2G, the ratio is 2 times of Bekenstein-Hawking entropy-area formula in many cases of physical interest. In four dimensions, the universal relation is always true irrespective of the coefficients of the higher-order terms if the dilaton couplings are the same, which is the case for string effective theory, while in five dimensions, the relation again holds irrespective of the overall coefficient if the higher-order corrections are in the GB combination. We also discuss how this result generalizes to known physically interesting cases with Lovelock correction terms in various dimensions, and possible implications of the universal relation.

We study primordial perturbations generated from quantum fluctuations of an inflaton based on the formalism of stochastic gravity. Integrating out the degree of freedom of the inflaton field, we analyze the time evolution of the correlation function of the curvature perturbation at tree level and compare it with the prediction made by the gauge-invariant linear perturbation theory. We find that our result coincides with that of the gauge-invariant perturbation theory if the e-folding from the horizon-crossing time is smaller than some critical value (similar to vertical bar slow-roll parameter vertical bar(-1)), which is the case for the scales of the observed cosmological structures. However, in the limit of the superhorizon scale, we find a discrepancy in the curvature perturbation, which suggests that we should include the longitudinal part of the gravitational field in the quantization of a scalar field even in stochastic gravity.

We study collision of two domain walls in five-dimensional (5D) spacetime and creation of matter fields. This may provide the reheating mechanism in cosmological models based on a colliding-brane scenario such as the ekpyrotic (or cyclic) universe.
We first analyze the dynamics of colliding domain walls both in 5D Minkowski background spacetime and in asymptotic AdS spacetime including self-gravity. We find that multiple bounces appear at collision. In the case with gravity, we find that a spacelike curvature singularity is formed in the bulk, but it is covered by a horizon.
Next we analyze production of particles at collision of two domain walls. For a scalar 0 where g is a field, the energy density of created particles is evaluated as rho approximate to 20(g)(-4) Nb m(Phi)(4) coupling constant of particles to a domain-wall scalar field, Nb is the number of bounces at the collision and m Phi is a fundamental mass scale of the domain wall. We also study the behaviour, of 5D fermions localized on domain walls, when two walls collide in a 5D Minkowski background spacetime. For kappa = 0 mode, we find that most fermions are localized on both branes as a whole even after collision. However, how much fermions are localized on which brane depends sensitively on the incident velocity and the coupling constants.

We study gravitational waves from a particle moving around a system of a point mass with a disk in Newtonian gravitational theory. A particle motion in this system can be chaotic when the gravitational contribution from a surface density of a disk is comparable with that from a point mass. In such an orbit, we sometimes find that there appears a phase in which particle motion becomes nearly regular (so-called "stagnant motion" or stickiness) for a finite time interval between more strongly chaotic phases. To study how these different chaotic behaviors affect observation of gravitational waves, we investigate a correlation of the particle motion and the waves. We find that such a difference in chaotic motions reflects on the wave forms and energy spectra. The character of the waves in the stagnant motion is quite different from that either in a regular motion or in a more strongly chaotic motion. This suggests that we may make a distinction between different chaotic behaviors of the orbit via the gravitational waves.

We study the behaviour of five-dimensional fermions localized on branes, which we describe by domain walls, when two parallel branes collide in a five-dimensional Minkowski background spacetime. We find that most fermions are localized on both branes as a whole even after collision. However, how much fermions are localized on which brane depends sensitively on the incident velocity and the coupling constants unless the fermions exist on both branes. (c) 2007 Elsevier B.V. All rights reserved.

We study the dynamics of colliding domain walls including self-gravity. The initial data is set up by applying a Bogomol'nyi-Prasad-Sommerfield (BPS) domain wall in five-dimensional supergravity, and we evolve the system determining the final outcome of collisions. After a collision, a spacelike curvature singularity covered by a horizon is formed in the bulk, resulting in a black brane with trapped domain walls. This is a generic consequence of collisions, except for nonrelativistic weak field cases, in which the walls pass through one another or multiple bounces take place without singularity formation. These results show that incorporating the self-gravity drastically changes a naive picture of colliding branes.

We construct a supersymmetric rotating black hole with asymptotically flat four-dimensional spacetime times a circle, by superposing an infinite number of BMPV black hole solutions at the same distance in one direction. The near-horizon structure is the same as that of the five-dimensional BMPV black hole. The rotation of this black hole can exceed the Kerr bound in general relativity (q equivalent to a/G(4)M=1), if the size is small.

We present a detailed study of inflationary solutions in M theory with higher order quantum corrections. We first exhaust all exact and asymptotic solutions of exponential and power-law expansions in this theory with quartic curvature corrections, and then perform a linear perturbation analysis around fixed points for the exact solutions in order to see which solutions are more generic and give interesting cosmological models. We find an interesting solution in which the external space expands exponentially and the internal space is static both in the original and Einstein frames. Furthermore, we perform a numerical calculation around this solution and find numerical solutions which give enough e-foldings. We also briefly summarize similar solutions in type II superstrings.

We study collision of two domain walls in five-dimensional asymptotically anti-de Sitter spacetime. This may provide the reheating mechanism of an ekpyrotic (or cyclic) brane universe, in which two Bogomol'nyi-Prasad-Sommerfield branes collide and evolve into a hot big bang universe. We evaluate a change of scalar field making the domain wall and can investigate the effect of a negative cosmological term in the bulk to the collision process and the evolution of our universe.

We study a stationary "black" brane in M/superstring theory. Assuming BPS-type relations between the first-order derivatives of metric functions, we present general stationary black brane solutions with a traveling wave for the Einstein equations in D-dimensions. The solutions are given by a few independent harmonic equations (and plus the Poisson equation). General solutions are constructed by superposition of a complete set of those harmonic functions. Using the hyperspherical coordinate system, we explicitly give the solutions in 11-dimensional M theory for the case with M2⊥M5 intersecting branes and a traveling wave. Compactifying these solutions into five dimensions, we show that these solutions include the BMPV black hole and the Brinkmann wave solution. We also find new solutions similar to the Brinkmann wave. We prove that the solutions preserve the 1/8 supersymmetry if the gravi-electromagnetic field ℱij, which is a rotational part of gravity, is self-dual. We also discuss non-spherical "black" objects (e.g., a ring topology and an elliptical shape) by use of other curvilinear coordinates. © 2006 IOP Publishing Ltd.

We study a stationary "black" brane in M/superstring theory. Assuming BPS-type relations between the first-order derivatives of metric functions, we present general stationary black brane solutions with a traveling wave for the Einstein equations in D-dimensions. The solutions are given by a few independent harmonic equations (and plus the Poisson equation). General solutions are constructed by superposition of a complete set of those harmonic functions. We prove that the solutions preserve the 1/8 supersymmetry if the gravi-electromagnetic field F-ij, which is a rotational part of gravity, is self-dual.

We investigate a creation of a brane world with a bulk scalar field. We consider an exponential potential of a bulk scalar field; V(phi) proportional to exp(-2 beta phi), where beta is the parameter of the theory. This model is based on a supersymmetric theory, and includes Randall-Sundrum model (beta = 0) and the 5-dimensional effective model of the Horva-Witten theory (beta = 1). We show that for this potential a brane instanton is constructed only when a curvature of a brane vanishes, that is, the brane is flat. We construct an instanton with two branes and a singular instanton with a single brane. The Euclidean action of the singular instanton solution is finite if beta(2) &gt; 2/3. We also calculate perturbations of the action around a singular instanton solution in order to show that the singular instanton is well-defined.

Studying Yang-Mills field in Bianchi spacetime, we find that Yang-Mills field shows chaotic behaviors in the Einstein-Yang-Mills (EYM) system. We also analyze a multiplicative effect by two types of chaos, that is, chaos found with Yang-Mills field and that found in Bianchi IX spacetime. Although we find that chaotic behavior of Yang- Mills field in such a system, two types do not coexist, resulting that no enhancement is obtained.

We study the coevolution of Yang-Mills fields and perfect fluids in Bianchi type I universes. We investigate numerically the evolution of the universe and the Yang-Mills fields during the radiation and dust eras of a universe that is almost isotropic. The Yang-Mills field undergoes small amplitude chaotic oscillations, as do the three expansion scale factors which are also displayed by the expansion scale factors of the universe. The results of the numerical simulations are interpreted analytically and compared with past studies of the cosmological evolution of magnetic fields in radiation and dust universes. We find that, whereas magnetic universes are strongly constrained by the microwave background anisotropy, Yang-Mills universes are principally constrained by primordial nucleosynthesis but the bound is comparatively weak with Omega(YM)&lt; 0.105 Omega(rad).

We study the evolution of a five-dimensional rotating black hole emitting scalar field radiation via the Hawking process for arbitrary initial values of the two rotation parameters a and b. It is found that any such black hole whose initial rotation parameters are both nonzero evolves toward an asymptotic state a/M-l/2 = b/M-1/2 = const(not equal 0), where this constant is independent of the initial values of a and b.

We analyze the energy extraction by the Penrose process in higher dimensions. Our result shows the efficiency of the process from higher dimensional black holes and black rings can be rather high compared with that in the four-dimensional Kerr black hole. In particular, if one rotation parameter vanishes, the maximum efficiency becomes infinitely large because the angular momentum is not bounded from above. We also apply a catastrophe theory to analyze the stability of black rings. It indicates a branch of black rings with higher rotational energy is unstable, which should be a different type of instability from the Gregory-Laflamme one.

Studying the Yang-Mills field and the gravitational field in class A Bianchi spacetimes, we find that chaotic behavior appears in the late phase (the asymptotic future). In this phase, the Yang-Mills field behaves as that in Minkowski spacetime, in which we can understand it by a potential picture, except for types VIII and IX. At the same time, in the initial phase (near the initial singularity), we numerically find that the behavior seems to approach the Kasner solution. However, we show that the Kasner circle is unstable and the Kasner solution is not an attractor. From an analysis of stability and numerical simulation, we find a Mixmaster-like behavior in Bianchi I spacetime. Although this result may provide a counterexample to the Belinskii, Khalatnikov, and Lifshitz (BKL) conjecture, we show that the BKL conjecture is still valid in Bianchi IX spacetime. We also analyze a multiplicative effect of two types of chaos, that is, chaos with the Yang-Mills field and that in vacuum Bianchi IX spacetime. Two types of chaos seem to coexist in the initial phase. However, the effect due to the Yang-Mills field is much smaller than that of the curvature term.

We study time-dependent solutions in M and superstring theories with higher-order corrections. We first present general field equations for theories of Lovelock type with stringy corrections in arbitrary dimensions. We then exhaust all exact and asymptotic solutions of exponential and power-law expansions in the theory with Gauss-Bonnet terms relevant to heterotic strings and in the theories with quartic corrections corresponding to the M theory and type II superstrings. We discuss interesting inflationary solutions that can generate enough e foldings in the early universe.

We study particle production at the collision of two domain walls in 5-dimensional Minkowski spacetime. This may provide the reheating mechanism of an ekpyrotic (or cyclic) brane universe, in which two BPS branes collide and evolve into a hot big bang universe. We evaluate a production rate of particles confined to the domain wall. The energy density of created particles is given as rhoapproximate to20 (g) over bar (4)N(b)m(eta)(4) where (g) over bar is a coupling constant of particles to a domain-wall scalar field, N-b is the number of bounces at the collision and m(eta) is the fundamental mass scale of the domain wall. It does not depend on the width d of the domain wall, although the typical energy scale of created particles is given by omegasimilar to1/d. The reheating temperature is evaluated as T(R)approximate to0.88 (g) over barN(b)(1/4). In order to have the baryogenesis at the electro-weak energy scale, the fundamental mass scale is constrained as m(eta)greater than or similar to1.1x10(7) GeV for (g) over bar similar to10(-5).

Here we study the creation of a brane world using an instanton solution with Hartle-Hawking's no-boundary approach. We analyze brane models with a Gauss-Bonnet term in a bulk spacetime. The curvature of 3-brane is assumed to be closed, flat, or open. We construct instanton solutions with branes for our models, and calculate the value of the actions to discuss the initial state of a brane universe.

We study brane cosmology as 4D (four-dimensional) domain-wall dynamics in 5D bulk spacetime. For a generic 5D bulk with 3D maximal symmetry, we derive the equation of motion of a domain wall and find that it depends on mass function of the bulk spacetime, and the energy-momentum conservation in a domain wall is affected by a lapse function in the bulk. Especially, for a bulk spacetime with nontrivial lapse function, energy of matter field on the domain wall goes out or comes in from the bulk spacetime. Applying our result to the case with SU(2) gauge bulk field, we obtain a singularity-free universe in brane world scenario, that is, not only a big bang initial singularity of the brane is avoided but also a singularity in a 5D bulk does not exist.

To investigate how chaos affects gravitational waves, we study the gravitational waves from a spinning test particle moving around a Kerr black hole, which is a typical chaotic system. To compare the result with those in a nonchaotic dynamical system, we also analyze a spinless test particle, whose orbit can be complicated in the Kerr back ground although the system is integrable. We estimate the emitted gravitational waves by the multipole expansion of a gravitational field. We find a striking difference in the energy spectra of the gravitational waves. The spectrum for a chaotic orbit of a spinning particle contains various frequencies, while some characteristic frequencies appear in the case of a spinless particle.

We study inflationary solutions in the M-theory. Including the fourth-order curvature correction terms, we find three generalized de Sitter solutions, in which our 3-space expands exponentially. Taking one of the solutions, we propose an inflationary scenario of the early universe. This provides us a natural explanation for large extra dimensions in a brane world, and suggests some connection between the 60 e-folding expansion of inflation and TeV gravity based on the large extra dimensions. (C) 2004 Elsevier B.V. All rights reserved.

It has been known that a B=2 skyrmion is axially symmetric. We consider the Skyrme model coupled to gravity and obtain static axially symmetric regular and black hole solutions numerically. Computing the energy density of the skyrmion, we discuss the effect of gravity to the energy density and baryon density of the skyrmion.

Here we study the creation of a brane world using an instanton solution with Hartle-Hawking’s no-boundary approach. We analyze brane models with a Gauss-Bonnet term in a bulk spacetime. The curvature of 3-brane is assumed to be closed, flat, or open. We construct instanton solutions with branes for our models, and calculate the value of the actions to discuss the initial state of a brane universe. © 2004 The American Physical Society.

We investigate a stabilization of extra dimensions in a ten-dimensional Kaluza-Klein theory and type IIB supergravity. We assume (A)dS(5)xS(5) compactification, and calculate quantum effects to find an effective potential for the radius of internal space. The effective potential has a minimum, and if the universe is created on the top of the potential hill, the universe evolves from dS(5) to AdS(5) after exponential expansion. The internal space S-5 stays small and its radius becomes constant. Our model in type IIB supergravity contains the 4-form gauge field with a classical vacuum expectation value, which is the role of a ten-dimensional cosmological constant. If the universe evolves into anti-de Sitter, the five-dimensional Randall-Sundrum setup with a stabilized dilaton is obtained from the type IIB supergravity model.

We perform a linear perturbation analysis for black hole solutions with a "massive" Yang-Mills field (the Proca field) in Brans-Dicke theory and find that the results are quite consistent with those via catastrophe theory where thermodynamic variables play an intrinsic role. Based on this observation, we show the general relation between these two methods in generalized theories of gravity which are conformally related to the Einstein-Hilbert action.

We present the effective equations to describe the four-dimensional gravity of a brane world, assuming that a five-dimensional bulk spacetime satisfies the Einstein equations and gravity is confined on the Z(2) symmetric brane. Applying this formalism, we study the induced-gravity brane model first proposed by Dvali, Gabadadze, and Porrati. In a generalization of their model, we show that an effective cosmological constant on the brane can be extremely reduced in contrast with the case of the Randall-Sundrum model even if a bulk cosmological constant and a brane tension are not fine tuned.

We study the five-dimensional Einstein-Yang-Mills system with a cosmological constant. Assuming a spherically symmetric spacetime, we find a new analytic black hole solution, which approaches asymptotically "quasi-Minkowski," "quasi-anti-de Sitter," or "quasi-de Sitter" spacetime depending on the sign of the cosmological constant. Since there is no singularity except for the origin that is covered by an event horizon, we regard it as a localized object. This solution corresponds to a magnetically charged black hole. We also present a singularity-free particlelike solution and a nontrivial black hole solution numerically. Those solutions correspond to the Bartnik-McKinnon solution and a colored black hole with a cosmological constant in four dimensions. We analyze their asymptotic behavior, spacetime structures, and thermodynamical properties. We show that there is a set of stable solutions if the cosmological constant is negative.

We study the dynamics of a scalar field in brane cosmology. We assume that the scalar field is confined in our four-dimensional world. As for the potential of the scalar field, we discuss three typical models: (1) a power-law potential, (2) an inverse-power-law potential, and (3) an exponential potential. We show that the behavior of the scalar field is very different from that in conventional cosmology when the energy density square of the term dominates.

We present effective equations to describe the four-dimensional gravity of a brane world, assuming that a five-dimensional bulk spacetime satisfies the Einstein equations and gravity is confined on the Z_2 symmetric brane. Applying this formalism to the Randall-Sundrum brane world model, we find two new additional terms in the Einstein equations : One is the quadratic term of the energy-momentum tensor of matter field and the other is the 5-dimensional Weyl curvature term. Although the four-dimensional effective equations are not closed and further information from the bulk is required, those terms may provide us windows to search for extra dimensions. We discuss some effects of those terms on cosmology and compact objects. Since those additional terms appear naturally from the present reduction, we apply it to other brane models. We study three models ; the model with a bulk dilaton field motivated by Horava-Witten model, the induced gravity brane model of Dvali, Gabadadze and Porrati, and the R^2 inflationary model proposed by Starobinsky.

We investigate spherically symmetric self-similar solutions in Brans-Dicke theory. Assuming a perfect fluid with the equation of state p=(gamma-1)mu(1less than or equal togamma&lt;2), we show that there are no nontrivial solutions which approach asymptotically to the flat Friedmann-Robertson-Walker spacetime if the energy density is positive. This result suggests that primordial black holes in Brans-Dicke theory cannot grow at the same rate as the size of the cosmological particle horizon.

We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve the hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method up to second order. This perturbative approach is an extension of the usual Lagrangian perturbation theory for a pressureless fluid, in view of the inclusion of the pressure effect, which should be taken into account on the occurrence of velocity dispersion. We obtain the first-order solutions in generic background universes and the second-order solutions in a wider range of a polytropic index, whereas our previous work gives the first-order solutions only in the Einstein-de Sitter background and the second-order solutions for the polytropic index 4/3. Using the perturbation solutions, we present illustrative examples of our formulation in one- and two-dimensional systems, and discuss how the evolution of inhomogeneities changes for the variation of the polytropic index.

We consider the collision of self-gravitating n -branes in a (n + 2) -dimensional spacetime. We show that there is a geometrical constraint which can be expressed as a simple sum rule for angles characterizing Lorentz boosts between branes and the intervening spacetime regions. This constraint can then be reinterpreted as either energy or momentum conservation at the collision.

We calculate quasinormal f and g modes of a neutron star with density discontinuity, which may appear in a phase transition at an extremely high density. We find that discontinuity will reflect largely on the f mode, and that the g mode could also be important for a less massive star.

We study a new quintessence scenario by a scalar field with an inverse-power potential based on the brane cosmology. We show that in the quadratic dominant stage, which generically appears in brane world cosmology, the density parameter of a scalar field Omega(phi) decreases regardless of the potential-term contribution. This feature enables us to impose natural initial condition. We also discuss the constraints on parameters for the natural and successful quintessence scenario. (1)).

We reanalyze a new quintessence scenario in a brane world model, assuming that a quintessence scalar field is confined in our three-dimensional brane world. We study three typical quintessence models: (1) an inverse-power-law potential, (2) an exponential potential, and (3) a kinetic-term quintessence (k-essence) model. With an inverse-power-law potential model [V(phi) = mu (alpha +4)phi (-alpha)], we show that in the quadratic dominant stage the density parameter of a scalar field Omega (phi) decreases as a(-4(alpha -2)/(alpha +2)) for 2&lt;&lt;alpha&gt;&lt;6, which is followed by the conventional quintessence scenario. This feature provides us wider initial conditions for successful quintessence. In fact, even if the universe is initially scalar-field dominated, it eventually evolves into a radiation dominated era in the &lt;rho&gt;(2)-dominant stage. Assuming an equipartition condition, we discuss constraints on parameters, with the result that alpha greater than or equal to4 is required. This constraint also restricts the value of the five-dimensional Planck mass, e.g., 4x10(-14)m(4)less than or similar tom(5)less than or similar to 3x10(-13)m(4) for alpha =5. For an exponential potential model V =mu (4) exp(-lambda phi /m(4)), we may not find a natural and successful quintessence scenario as it is, while for a kinetic-term quintessence, we find a tracking solution even in the rho (2)-dominant stage, rather than the Omega (phi)-decreasing solution for an inverse-power-law potential. Then we do find a slight advantage in a brane world. Only the density parameter increases more slowly in the rho (2)-dominant stage, which provides a wider initial condition for successful quintessence.

We propose a new quintessence scenario in brane cosmology, assuming that a quintessence field Q is confined in our three-dimensional brane world. With a potential V(Q)=mu (alpha +4)Q(-alpha) (alpha greater than or equal to2), we find that the density parameter of the scalar field decreases as Omega (Q)similar toa(-4(alpha -2)/(alpha +2)) in the epoch of quadratic energy density dominance, if alpha less than or equal to6. This attractor solution is followed by the usual tracking quintessence scenario after a conventional Friedmann universe is recovered. With an equipartition of initial energy density, we find a natural and successful quintessence model for alpha greater than or similar to4.

We consider the internal structure of the Skyrme black hole under a static and spherically symmetric ansatz. We concentrate on solutions with node number 1 and with "winding" number 0, where there exist two solutions for each horizon radius, one solution is stable and the other is unstable against linear perturbation. We find that a generic solution exhibits an oscillating behavior near the singularity, similar to a solution in the Einstein-Yang-Mills (EYM) system, and independent of the stability of the solution. Comparing it with that in the EYM system, this oscillation becomes mild because of the mass term of the Skyrme field. We also find Schwarzschild-like exceptional solutions where no oscillating behavior is seen. Contrary to the EYM system where there is one such solution branch if the node number is fixed, there are two branches corresponding to the stable and unstable ones.

We study brane-world preheating in a massive chaotic inflationary scenario where scalar fields are confined on the three-brane. Assuming that the quadratic contribution in energy densities dominates the Hubble expansion rate during preheating, the amplitude of the inflaton decreases slowly relative to the standard dust-dominated case. This leads to an efficient production of chi particles via the nonperturbative decay of the inflaton even if its coupling is of the order of g = 10(-5). We also discuss massive particle creation heavier than the inflaton, which may play an important role for baryogenesis and leptogenesis scenarios.

We use a perturbation method to study gravitational waves from a spinning test particle scattered by a relativistic star. The present analysis is restricted to axial modes. By calculating the energy spectrum, the wave forms, and the total energy and angular momentum of gravitational waves, we analyze the dependence of the emitted gravitational waves on particle spin. For a normal neutron star, the energy spectrum has one broad peak whose characteristic frequency corresponds to the angular velocity at the turning point (a periastron). Since the turning point is determined by the orbital parameter, there exists a dependence of the gravitational wave on particle spin. We find that the total energy of l = 2 gravitational waves gets larger as the spin increases in the antiparallel direction to the orbital angular momentum. For an ultracompact star, in addition to such an orbital contribution, we find the quasinormal modes excited by a scattered particle, whose excitation rate to gravitational waves depends on the particle spin. We also discuss the ratio of the total angular momentum to the total energy of gravitational waves and explain its spin dependence.

We use a perturbation method to study gravitational waves from a spinning test particle scattered by a relativistic star. The present analysis is restricted to axial modes. By calculating the energy spectrum, the wave forms, and the total energy and angular momentum of gravitational waves, we analyze the dependence of the emitted gravitational waves on particle spin. For a normal neutron star, the energy spectrum has one broad peak whose characteristic frequency corresponds to the angular velocity at the turning point (a periastron). Since the turning point is determined by the orbital parameter, there exists a dependence of the gravitational wave on particle spin. We find that the total energy of l = 2 gravitational waves gets larger as the spin increases in the antiparallel direction to the orbital angular momentum. For an ultracompact star, in addition to such an orbital contribution, we find the quasinormal modes excited by a scattered particle, whose excitation rate to gravitational waves depends on the particle spin. We also discuss the ratio of the total angular momentum to the total energy of gravitational waves and explain its spin dependence.

We consider black hole solutions in the SU(3) Einstein-Yang-Mills-dilaton system under the static and spherically symmetric ansatz. We reveal some properties which were not investigated before. In particular, we find that there appears a shell-like structure in the energy density distribution outside the horizon which can be interpreted as a symptom of the instability of black holes.

The two-point correlation function of galaxy distribution shows that structure in the present universe is scale-free up to a certain scale (at least several tens of Mpc), which suggests that a fractal structure may exist. If small primordial density fluctuations have a fractal structure, the present fractal-like nonlinear structure below the horizon scale could be naturally explained. We analyze the time evolution of fractal density perturbations in an Einstein-de Sitter universe, and study how the perturbation evolves and what kind of nonlinear structure will result. We assume a one-dimensional collisionless sheet model with initial Cantor-type fractal perturbations. The nonlinear structure seems to approach some attractor with a unique fractal dimension, which is independent of the fractal dimensions of initial perturbations. A discrete self-similarity in the phase space is also found when the universal nonlinear fractal structure is reached.

We carefully investigate the gravitational equations of the brane world, in which all the matter forces except gravity are confined on the 3-brane in a 5-dimensional spacetime with Z(2) symmetry. We derive the effective gravitational equations on the brane, which reduce to the conventional Einstein equations in the low energy limit. From our general argument we conclude that the first Randall-Sundrum-type theory predicts that the brane with a negative tension is an antigravity world and hence should be excluded from the physical point of view. Their second-type theory where the brane has a positive tension provides the correct signature of gravity. In this latter case, if the bulk spacetime is exactly anti-de Sitter spacetime, generically the matter on the brane is required to be spatially homogeneous because of the Bianchi identities. By allowing deviations from anti-de Sitter spacetime in the bulk, the situation will be relaxed and the Bianchi identities give just the relation between the Weyl tensor and the energy momentum tensor. In the present brane world scenario, the effective Einstein equations cease to be valid during an era when the cosmological constant on the brane is not well defined, such as in the case of the matter dominated by the potential energy of the scalar field.

We find the explicit coordinate transformation which links two exact cosmological solutions of the brane world which have been recently discovered. This means that both solutions are exactly the same as each other. One of the two solutions is described by the motion of a domain wall in the well-known five-dimensional Schwarzshild-AdS spacetime. Hence, we can easily understand the region covered by the coordinate used by another solution.

We carefully investigate the gravitational perturbation of the Randall-Sundrum (RS) single brane-world solution [L. Randell and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999)], based on a covariant curvature tensor formalism recently developed by us. Using this curvature formalism, it is known that the "electric" part of the five-dimensional Weyl tensor, denoted by E-mu nu, gives the leading order correction to the conventional Einstein equations on the brane. We consider the general solution of the perturbation equations for the five-dimensional Weyl tensor caused by the matter fluctuations on the brane. By analyzing its asymptotic behavior in the direction of the fifth dimension, we find the curvature invariant diverges as we approach the Cauchy horizon. However, in the limit of asymptotic future in the vicinity of the Cauchy horizon, the curvature invariant falls off fast enough to render the divergence harmless to the brane world. We also obtain the asymptotic behavior of E-mu nu on the brane at spatial infinity, assuming that the matter perturbation is localized. We find it falls off sufficiently fast and will not affect the conserved quantities at spatial infinity. This indicates strongly that the usual conservation law, such as the ADM energy conservation, holds on the brane as far as asymptotically flat spacetimes are concerned.

In the one-loop string effective action, we study a generality of nonsingular cosmological solutions found in the isotropic and homogeneous case. We discuss Bianchi type-I and -IX spacetimes. We find that nonsingular solutions still exist in the Bianchi type-I model around nonsingular flat Friedmann solutions. On the other hand, we cannot find any nonsingular solutions in the Bianchi type-IX model. The nonexistence of a nonsingular Bianchi type-IX universe may be consistent with the analysis of Kawai, Sakagami, and Soda; i.e., the tensor-mode perturbations against a nonsingular flat Friedmann universe are unstable, because the Bianchi type-IX model is regarded as a closed Friedmann universe with a single gravitational wave. With the stability analysis of Kawai, Sakagami, and Soda, the nonsingular universe found in the isotropic case is unstable, and a singularity avoidance may not work in generic spacetimes.

A spinning test particle around a Schwarzschild black hole shows chaotic behavior if its spin is larger than a critical value. We discuss whether or not some peculiar signature of chaos appears in the gravitational waves emitted from such a system. Calculating the emitted gravitational waves by use of the quadrupole formula, we find that the energy emission rate of gravitational waves for a chaotic orbit is about 10 times larger than that for a circular orbit, but the same enhancement is also obtained by a regular "elliptic" orbit. A chaotic motion does not always enhance the energy emission rate maximally. As for the energy spectra of the gravitational waves, we find some characteristic feature for a chaotic orbit. It may tell us how to find the chaotic behavior of the system. Such peculiar behavior, if it is found, may also provide some additional information to determine the parameters of a system such as a spin.

In higher-curvature inflation models (R + alpha(n)R(n)), we study a parametric preheating of a scalar field chi coupled nonminimally to a spacetime curvature R(xi R chi(2)). In the case of the R-2-inflation model, efficient preheating becomes possible for rather small values of xi, i.e., \xi\less than or similar to several. Although the maximal fluctuation root[chi(2)](max)approximate to 2x10(17) GeV for xi approximate to -4 is almost the same as the chaotic inflation model with a nonminimally coupled chi held, the growth rate of the fluctuation becomes much larger and efficient preheating is realized. We also investigate preheating for the R-4 model and find that the maximal fluctuation is root[chi(2)](max) approximate to 8 x 10(16) GeV for xi approximate to -35. [S0556-2821(99)05522-8].

We find a self-gravitating monopole and its black hole solution in Brans-Dicke (BD) theory. We mainly discuss the properties of these solutions in the Einstein frame and compare the solutions with those in general relativity (GR) on the following points. From the held distributions of the generic type of self-gravitating monopole solutions, we find that the Yang-Mills potential and the Higgs field hardly depend on the ED parameter for most of the solution. There is an upper Limit of the vacuum expectation value of the Higgs field to which a solution exists, as in GR. Since the ED scalar field has the effect of lessening an effective gauge charge, the upper limit in ED theory (in the omega=0 case) becomes about 30% larger than in GR. In some parameter ranges, then are two nontrivial solutions with the same mass, one of which can be regarded as the excited state of the other. This is confirmed by the analysis by catastrophe theory, which states that the excited solution is unstable. We also find that the ED scalar field varies more for solutions of smaller horizon radii, which can be understood from the differences of the nontrivial structure outside the horizon. A scalar mass and the thermodynamical properties of new solutions are also examined. Our analysis may give insight into solutions in other theories of gravity; particularly, a theory with a dilaton field may show similar effects because of its coupling to a gauge field. [S0556-2821(99)07220-3].

We investigate the resonant particle production of a scalar field chi coupled nonminimally to a spacetime curvature R (xi R chi(2)) as well as to an inflaton field phi (g(2)phi(2)chi(2)) In the case of g less than or similar to 3 x 10(-4), the xi effect assists g resonance in certain parameter regimes. However, for g greater than or similar to 3 x 10(-4), g resonance is not enhanced by the xi effect because of the xi suppression effect as well as a back reaction effect. If xi approximate to -4, the maximal fluctuation of produced chi particles is root[chi(2)](max) approximate to 2 x 10(17) GeV for g less than or similar to 1 x 10(-5), which is larger than the minimally coupled case with g approximate to 1 x 10(-3). [S0556-2821(99)00618-9].

Using a metric perturbation method, we study gravitational waves from a test particle scattered by a spherically symmetric relativistic star. We calculate the energy spectrum and the waveform of gravitational waves for axial modes. Since metric perturbations in axial modes do not couple to the matter fluid of the star, emitted waves for a normal neutron star show only one peak in the spectrum, which corresponds to the orbital frequency at the turning point, where the gravitational field is strongest. However, for an ultracompact star (the radius R less than or similar to 3M), another type of resonant periodic peak appears in the spectrum. This is just because of an excitation by a scattered particle of axial quasinormal modes, which were found by Chandrasekhar and Ferrari. This excitation comes from the existence of the potential minimum inside of a star. We also find for an ultracompact star many small periodic peaks at the frequency region beyond the maximum of the potential, which would be due to a resonance of two waves reflected by two potential barriers (Regge-Wheeler type and one at the center of the star). Such resonant peaks appear neither for a normal neutron star nor for a Schwarzschild black hole. Consequently, even if we analyze the energy spectrum of gravitational waves only for axial modes, it would be possible to distinguish between an ultracompact star and a normal neutron star (or a Schwarzschild black hole). [S0556-2821(99)06612-6].

According to previous work, topological defects expand exponentially without end if the vacuum expectation value of the Higgs field is of the order of the Planck mass. We extend the study of inflating topological defects to Brans-Dicke gravity. With the help of numerical simulations we investigate the dynamics and spacetime structure of a global monopole. Contrary to the case of Einstein gravity, any inflating monopole eventually shrinks and takes a stable configuration. We also discuss cosmological constraints on the model parameters. [S0556-2821(99)05410-7].

The decay of a metastable false vacuum by bubble nucleation is studied in the high temperature limit of the gauge theory in which an SO(3) gauge symmetry is spontaneously broken to an SO(2). The effects of internal symmetry are so drastic that, in addition to the known Euclidean bounce solution, there exists a new bubble solution involving a 't Hooft-Polyakov monopole at its center the moment it is nucleated. The decay rate and evolution are analyzed. (C) 1999 Published by Elsevier Science B.V, All rights reserved.

We give an explicit formulation of the three-dimensional SL(4,R)/SO(2,2) sigma-model representing the five-dimensional Einstein gravity coupled to the dilaton and the three-form field for spacetimes with two commuting Killing vector fields. New matrix representation is obtained which is similar to one found earlier in the four-dimensional Einstein-Maxwell-Dilaton-Axion (EMDA) theory. The SL(4,R) symmetry joins a variety of 5D solutions of different physical types including strings, 0-branes, KK monopoles etc. interpreting them as duals to the four-dimensional Kerr metric translated along the fifth coordinate. The symmetry transformations are used to construct new rotating strings and composite (0-1)-branes endowed with a NUT parameter. (C) 1999 Published by Elsevier Science B.V. All rights reserved.

We investigate the stability of black hole solutions in an effective theory derived from a superstring model, which includes a dilaton field and the Gauss-Bonnet term. The critical solution, below which mass no static solution exists, divides a family of solutions in the mass-entropy diagram into two. The upper branch approaches the Schwarzschild solution in the large mass limit, while the lower branch ends up with a singular solution which has a naked singularity. In order to investigate the stability of black hole solutions, we adopt two methods. The first one is catastrophe theory, with which we discuss the stability of non-Abelian black holes in general relativity. The present system is classified as a fold catastrophe, which is the simplest case. Following catastrophe theory, if we regard entropy and mass as the potential and the control parameter, respectively, we find the lower branch is more unstable than the upper branch. To confirm this, we study the second method, which is a linear perturbation analysis. We find an unstable mode only for the solutions in the lower branch. Hence, our investigation presents one example that catastrophe theory is also applicable for a generalized theory of gravity. [S0556-2821(98)02118-3].

Using a black hole (BH) perturbation approach, we numerically study gravitational waves from a spinning particle of mass mu and spin s on the equatorial plane plunging into a Kerr BH of mass M and spin a. When we take into account the particle spin s, (a) the motion of the particle changes due to the coupling effects between s and the orbital angular momentum L-z and between s and a, and also (b) the energy momentum tensor of the linearized Einstein equations changes. We calculate the total radiated energy, linear momentum, angular momentum, the energy spectrum, and waveform of gravitational waves, and we find the following features. (1) There are three spin coupling effects: between L-z and a, between s and L-z, and between s and a when s is considered. Among them, (L-z.a) coupling is the most important effect for the amount of gravitational radiation, and the other two effects are not as remarkable as the first one. However, these effects are still important; for example, the total radiated energy changes by a factor of similar to 2 for the case of a/M = 0.6, L-z/mu M = 1.5 if we change s from 0 to less than or similar to M. (2) For the case when one of the three spins (a, L-z, and s) is vanishing, the amount of gravitational radiation becomes larger (smaller) if spin axes of the other two are parallel (antiparallel). For the case when three spins are nonvanishing, the amount of gravitational radiation becomes maximum if all the axial directions of s, a, and L-z coincide. Thus, our calculations indicate that in a coalescence of two black holes(BHs) whose spins and orbital angular momentum are aligned, gravitational waves are emitted most efficiently. [S0556-2821(98)05216-3].

We analyze black hole thermodynamics in a generalized theory of gravity whose Lagrangian is an arbitrary function of the metric, the Ricci tensor, and a scalar field. We can convert the theory into the Einstein frame via a "Legendre" transformation or a conformal transformation. We calculate thermodynamical variables both in the original frame and in the Einstein frame, following the Iyer-Wald definition which satisfies the first law of thermodynamics. We show that all thermodynamical variables defined in the original frame are the same as those in the Einstein frame, if the spacetimes in both frames are asymptotically flat, regular, and possess event horizons with nonzero temperatures. This result may be useful to study whether the second law is still valid in the generalized theory of gravity. [S0556-2821(98)01618-X].

We apply the renormalization group (RG) method to examine the observable scaling properties in Newtonian cosmology. The original scaling properties of the equations of motion in our model are modified for averaged observables on constant time slices. in the RG flow diagram, we find three robust fixed points: Einstein-de Sitter, Milne, and quiescent fixed points. Their stability (or instability) property does not change under the effect of fluctuations. Inspired by the inflationary scenario in the early Universe, we see the Einstein-de Sitter fixed point with small fluctuations as the boundary condition at the horizon scale. Solving the RG equations under this boundary condition toward the smaller scales, we find a generic behavior of observables such that the density parameter Omega decreases, while the Hubble parameter H increases for a smaller averaging volume. The quantitative scaling properties are analyzed by calculating the characteristic exponents around each fixed point. Finally we argue the possible fractal structure of the Universe beyond the horizon scale.

We study the stability of circular orbits of spinning test particles in Kerr spacetime. We find that some of the circular orbits become unstable in the direction perpendicular to the equatorial plane, although the orbits are still stable in the radial direction. For the large spin case [S/mu M less than or similar to O(1)], the innermost stable circular orbit I (ISCO) appears before the minimum of the effective potential in the equatorial plane disappears. This changes the radius of the ISCO and therefore the frequency of the last circular orbit. [S0556-2821(98)04014-4].

We study the apparent horizon for two boosted black holes in asymptotically de Sitter space-time by solving the initial data on a space with punctures. We show that the apparent horizon enclosing both black holes is not formed if the conserved mass of the system (Abbott-Deser mass) is larger than a critical mass. The black hole with too large an AD mass therefore cannot be formed in asymptotically de Sitter space-time even though each black hole has any inward momentum. We also discuss the dynamical meaning of the AD mass by examining the electric part of the Weyl tensor (the tidal force) for various initial data.

We find a black hole solution with a non-Abelian field in Brans-Dicke theory. It is an extension of a non-Abelian black hole in general relativity. We discuss two non-Abelian fields: an "SU(2)" Yang-Mills field with a mass (Proca field) and the SU(2)X SU(2) Skyrme field. In both cases, as in general relativity, there are two branches of solutions, i.e., two black hole solutions with the same horizon radius. The masses of both black holes are always smaller than those in general relativity. A cusp structure in the mass-horizon radius (M-g-r(h)) diagram, which is a typical symptom of stability change in catastrophe theory, does not appear in the Brans-Dicke frame but is found in the Einstein conformal frame. This suggests that catastrophe theory may be simply applied for a stability analysis as it is if we use the variables in the Einstein frame. We also discuss the effects of the Brans-Dicke scalar field on black hole structure.

Analyzing test particles falling into a Kerr black hole, we study gravitational waves in Brans-Dicke theory of gravity. First we consider a test particle plunging with a constant polar angle into a rotating black hole and calculate the waveform and emitted energy of both scalar and tensor modes of gravitational radiation. We find that the waveform as well as the energy of the scalar gravitational waves weakly depends on the rotation parameter of a black hole a and on the polar angle. Second, using a model of a nonspherical dust shell of test particles falling into a Kerr black hole, we study when the scalar modes dominate. When a black hole is rotating, the tensor modes do not vanish even for a ''spherically symmetric'' shell; instead a slightly oblate shell minimizes their energy but with a nonzero finite value, which depends on the Kerr parameter a. As a result, we find that the scalar modes dominate only for highly spherical collapse, but they never exceed the tensor modes unless the Brans-Dicke parameter omega(BD)less than or similar to 750 for a/M=0.99 or unless omega(BD)less than or similar to 20000 for a/M=0.5, where M is the mass of a black hole. We conclude that the scalar gravitational waves with omega(BD)less than or similar to several thousands do not dominate except for very limited situations (observation from the face-on direction of a test particle falling into a Schwarzschild black hole or highly spherical dust shell collapse into a Kerr black hole). Therefore, observation of polarization is also required when we determine the theory of gravity by the observation of gravitational waves.

We study the motion of a spinning test particle in Schwarzschild spacetime, analyzing the Poincare map and the Lyapunov exponent. We find chaotic behavior for a particle with spin higher than some critical value (e.g., S-cr similar to 0.635 mu M for the total angular momentum J = 4 mu M), where mu and M are the masses of a particle and of a black hole, respectively. The inverse of the Lyapunov exponent in the most chaotic case is about five orbiral periods, which suggests that chaos of a spinning particle may become important in some relativistic astrophysical phenomena. The ''effective potential'' analysis enables us to classify the particle orbits into four types as follows. When the total angular momentum J is large, some orbits are bounded and the ''effective potentials'' are classified into two types: (B1) one saddle point (unstable circular orbit) and one minimal point (stable circular orbit) on the equatorial plane exist for small spin; and (B2) two saddle points bifurcate from the equatorial plane and one minimal point remains on the equatorial plane for large spin. When J is small, no bound orbits exist and the potentials are classified into another two types: (U1) no extremal paint is found for small spin; and (U2) one saddle point appears on the equatorial plane, which is unstable in the direction perpendicular to the equatorial plane, for large spin. The types (B1) and (U1) are the same as those for a spinless particle, but the potentials (B2) and (U2) are new types caused by spin-orbit coupling. The chaotic behavior is found only in the type (B2) potential. The ''heteroclinic orbit,'' which could cause chaos, is also observed in type (B2).

We study the stability of a contracting silent universe, which is a spacetime with irrotational dust and vanishing magnetic part of the Weyl tensor, H-ab=0. Two general relativistic backgrounds are analyzed: one is an attractor of silent universes, i.e., a locally Kasner spacetime, and the other is a particular class of inhomogeneous Szekeres solutions. In both cases their stabilities against perturbations with a nonzero magnetic part depend on a contraction configuration; a spindlelike collapse is unstable, while a pancakelike collapse is still stable. We also find that a similar instability exists in spindle collapse for a Newtonian case. We conclude that H-ab=0 is not a generic ansatz even in general relativistic dust collapse.

We discuss black holes in an effective theory derived from a superstring model, which includes a dilaton field, a gauge field, and the Gauss-Bonnet term. Assuming U(1) or SU(2) symmetry for the gauge field, we find four types of spherically symmetric solutions, i.e., a neutral, an electrically charged, a magnetically charged, and a “colored” black hole, and discuss their thermodynamical properties and fate via the Hawking evaporation process. For neutral and electrically charged black holes, we find a critical point and a singular end point. Below the mass corresponding to the critical point, no solution exists, while the curvature on the horizon diverges and a naked singularity appears at the singular point. A cusp structure in the mass-entropy diagram is found at the critical point and black holes on the branch between the critical and singular points become unstable. For magnetically charged and “colored” black holes, the solution becomes singular just at the end point with a finite mass. Because the black hole temperature is always finite even at the critical point or the singular point, we may conclude that the evaporation process will not be stopped even at the critical point or the singular point, and the black hole will move to a dynamical evaporation phase or a naked singularity will appear. © 1997 The American Physical Society.

We discuss black holes in an effective theory derived from a superstring model, which includes a dilaton field. a gauge field, and the Gauss-Bonnet term. Assuming U(1) or SU(2) symmetry for the gauge field, we find four types of spherically symmetric solutions, i.e., a neutral, an electrically charged, a magnetically charged, and a ''colored'' black hole, and discuss their thermodynamical properties and fate via the Hawking evaporation process. For neutral and electrically charged black holes, we find a critical point and a singular end point. Below the mass corresponding to the critical point. no solution exists, while the curvature on the horizon diverges and a naked singularity appears at the singular point. A cusp structure in the mass-entropy diagram is found at the critical point and black holes on the branch between the critical and singular points become unstable. For magnetically charged and ''colored'' black holes, the solution becomes singular just at the end point with a finite mass. Because the black hole temperature is always finite even at the critical point or the singular point, we may conclude that the evaporation process will not be stopped even at the critical; point or the singular point, and the black hole will move to a dynamical evaporation phase or a naked singularity will appear.

We study the motion of a test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (i) a local instability measured by the Weyl curvature, and (ii) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyse several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behaviour in some spacetimes, these can be accounted for by the second criterion.

We study the motion of a test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (i) a local instability measured by the Weyl curvature, and (ii) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyse several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behaviour in some spacetimes, these can be accounted for by the second criterion.

In this paper we examine the classical evolution of a cosmological model derived from the low-energy tree-level limit of a generic string theory. The action contains the metric, dilaton, central charge and an antisymmetric tensor field. We show that with a homogeneous and isotropic metric, allowing spatial curvature, there is a formal equivalence between this system and a scalar field minimally coupled to Einstein gravity in a spatially flat metric. We refer to this system as the shifted frame and using it we describe the full range of cosmological evolution that this model can exhibit. We show that generic solutions begin (or end) with a singularity. As the system approaches a singularity the dilaton becomes large and loop corrections will become important.

We study both spherically symmetric and rotating black holes with dilaton coupling and discuss the evaporation of these black holes via Hawking's quantum radiation and their fates. We find that the dilaton coupling constant alpha drastically affects the emission rates, and therefore the fates of the black holes. When the charge is conserved, the emission rate from the nonrotating hole is drastically changed beyond alpha = 1 (a superstring theory) and diverges in the extreme limit. In the rotating cases we analyze the slowly rotating black hole solution with arbitrary alpha as well as three exact solutions: the Kerr-Newman (alpha = 0), Kaluza-Klein (alpha = root 3), and Sen black hole (alpha = 1 and with axion field). Beyond the same critical value of alpha similar to 1, the emission rate becomes very large near the maximally charged limit, while for alpha &lt; 1 it remains finite. The black hole with alpha &gt; 1 may evolve into a naked singularity due to its large emission rate. We also consider the effects of a discharge process by investigating superadiance for the nonrotating dilatonic black hole.

We present spherically symmetric static solutions (a particlelike solution and a black-hole solution) of the Einstein-Yang-Mills system with a cosmological constant. Although their gravitational structures are locally similar to those of the Bartnik-McKinnon particles or the colored black holes, the asymptotic behavior becomes quite different because of the existence of a cosmological horizon. We also discuss their stability by means of a catastrophe theory as well as a linear perturbation analysis and find the number of unstable modes.

We study exotic black holes, which are new types of black holes obtained from unified theories. The exotic black holes we discussed here are classified into two; one is those with dilaton field, and the other contains non-Abelian ''gauge'' fields. We discuss their thermodynamical properties and evolutions. The farmer shows that the superstring predicts a critical dilaton coupling to U(1) field such that the Hawking radiation changes completely beyond the critical value and it diverges in the extreme limit. As a result, a naked singularity may appear at the end of evaporation process for models with larger coupling than the critical value.
The second type of exotic black holes give non-trivial black holes, which have the first type of hair. Since some of them are stable, this can be regarded as counterexamples of no hair conjecture. The specific heat will change the sign a few times for some range of parameters. The fate of those black holes are as follows:(1) The unstable black holes will becomes the other stable ones including Schwarzschild black hole. (2) The neutral black holes with the ''effective mass'' of non-Abelian fields have the upper bound of the black hole mass, and when the black hole evolves beyond this critical value, it shifts to more stable Schwarzschild black hole. If the black hole evaporates via the Hawking radiation, the stable particle will remain. (3) For the charged black hole such as monopole black hole, since the Reissner-Nordstrom black hole below some critical. mass becomes unstable and there is no Schwarzschild black hole, the monopole black hole is a unique and stable black hole in some range of parameters. When the black hot gets the mass via accretion, it will become the Reissner-Nordstrom trivial black hole, while when it evaporates via the Hawking radiation, the stable regular monopole will remain.

We present a new method for finding principal null directions (PNDs). Because our method assumes as an input the intrinsic metric and extrinsic curvature of a space-like hypersurface, we expect it will be useful to numerical relativists; We illustrate our method by finding the PNDs of the Kastor-Traschen spacetimes, which contain arbitrarily many Q = M black holes in a de Sitter background.

We consider a superradiance effect around rotating dilatonic black holes. We analyze two cases: one is an exact solution with the coupling constant alpha = root 3, which effective action is reduced from the 5-dimensional Kaluza-Klein theory, and the other is a slowly rotating dilatonic black holes with arbitrary coupling constant. We find that there exists a critical value (alpha similar to 1), which is predicted from a superstring model, and the superradiant emission rate with coupling larger than the critical value becomes much higher than the Kerr-Newman case (alpha = 0) in the maximally charged limit. Consequently, 4-dimensional primordial black holes in higher dimensional unified theories are either rotating but almost neutral or charged but effectively non-rotating.

We propose a hoop conjecture in the presence of a positive cosmological constant Lambda: when an apparent horizon forms in a gravitational collapse, the matter must be sufficiently compactified such that the circumference C satisfies the condition C less than or similar to 4 pi M less than or similar to 4 pi M(crit), where M is the Abbott-Deser mass of the collapsed body and M(crit) = 1/3 root Lambda. To confirm our conjecture, we investigate two cases; (1) initial data of a prolate or oblate dust spheroid, and (2) the Kastor-Traschen spacetime which describes a black hole collision with Lambda. We also discuss a relation between the hoop conjecture and an appearance of a naked singularity.

We complete a classification of junctions of two Friedmann-Robertson-Walker space-times bounded by a spherical thin wall. Our analysis covers superhorizon bubbles and thus complements the previous work of Berezin, Kuzumin, and Tkachev. Contrary to subhorizon bubbles, various topology types for superhorizon bubbles are possible, regardless of the sign of the extrinsic curvature. We also derive a formula for the peculiar velocity of a domain wall for all types of junction.

Using the covariant approach and conformal transformations, we present a gauge-invariant formalism for cosmological perturbations in generalized Einstein theories (GETs), including the Brans-Dicke theory, theories with a non-minimally coupled scalar field and certain curvature-squared theories. We find an enhancement in the growth rate of density perturbations in the Brans-Dicke theory and discuss attractive features of GETs in the structure formation process.

We study a generality of an inflationary scenario by integrating the Einstein equations numerically in a plane-symmetric spacetime. We consider the inhomogeneous spacetimes due to (i) localized gravitational waves with a positive cosmological constant LAMBDA and (ii) an inhomogeneous inflaton field PHI with a potential 1/2m2PHI2. For case (i), we find that any initial inhomogeneities are smoothed out even if waves collide, so that we conclude that inhomogeneity due to gravitational waves does not prevent the onset of inflation. As for case (ii), if the mean value of the inflaton field is initially as large as the condition in an isotropic and homogeneous inflationary model (i.e., the mean value is larger than several times the Planck mass), the field is soon homogenized and the universe always evolves into de Sitter spacetime. This supports the cosmic no hair conjecture in a planar universe. We also discuss the effects of an additional massless scalar field, which are introduced to set initial data in the usual analysis.

Two types of self-gravitating particle solutions found in several theories with non-Abelian fields are smoothly connected by a family of nontrivial black holes. There exists a maximum point of the black hole entropy where the stability of solutions changes. This criterion is universal, and the changes in stability follow from a catastrophe-theoretic analysis of the potential function defined by black hole entropy.

Developing a thin-wall formalism, we study the evolution of bubbles in extended inflation. We find the following two results. (1) Any true vacuum bubble expands, contrary to the results of Goldwirth and Zaglauer, who claim that bubbles created initially later collapse. We show that their initial conditions for collapsing bubbles are physically inconsistent. (2) Concerning the global space-time structure of the Universe in extended inflation, we show that wormholes are produced as in old inflation, resulting in the multiproduction of universes.

We present a formalism, encompassing an extension of Israel's thin-wall method, for studying the dynamics of bubbles in generalized Einstein theories. We use this formalism to show that in such theories, no bubble can be homogeneous both inside and out. The evolution equations are designed just in terms of variables in homogeneous outside. Only ordinary differential equations, including the initial constraints, arise from our formalism, which makes it useful for a variety of applications.

To investigate the cosmic no hair conjecture, we analyze numerically one-dimensional plane symmetrical inhomogeneities due to gravitational waves in vacuum spacetimes with a positive cosmological constant. Assuming periodic gravitational pulse waves initially, we study the time evolution of those waves and the nature of their collisions. As measures of inhomogeneity on each hypersurface, we use the three-dimensional Riemann invariant I = (3)R(ijkl) (3)R(ijkl) and the electric and magnetic parts of the Weyl tensor. We find a temporal growth of the curvature in the waves' collision region, but the overall expansion of the universe later overcomes this effect. No singularity appears and the result is a ''no hair'' de Sitter spacetime. The waves we study have amplitudes in the range 0.020LAMBDA less-than-or-equal-to I1/2 less-than-or-equal-to 125.0LAMBDA and widths in the range 0.080l(H) less-than-or-equal-to l less-than-or-equal-to 2.5l(H) where l(H) = (LAMBDA/3)-1/2, the horizon scale of de Sitter spacetime. This supports the cosmic no hair conjecture.

We present some black-hole solutions of the Einstein-Yang-Mills-dilaton system and calculate their Hawking temperatures. We find that if the coupling constant of the dilaton is smaller than some critical value, the thermodynamical behavior of these black holes includes two phase transitions at points determined by the value of the mass parameter. The black holes with masses between those two critical values have a positive specific heat. This is also true for the known colored black-hole solutions. We also reanalyze Skyrme black holes and find that there exist two types of solutions (a stable type and an unstable excited type) and these two types converge to a bifurcation point at some critical horizon radius, beyond which there is no Skyrme black hole. The stable black holes have two possible fates: they can evaporate via the Hawking process, and so evolve into a particlelike (Skyrmion) solution, or they can accrete matter and evolve into the Schwarzschild solution. When a Skyrme black hole evolves into a Schwarzschild black hole, its area changes discontinuously, so that we may regard this evolution as a kind of first-order phase transition. The specific heat of stable Skyrme black holes is always negative, while there are either one or three transition points for unstable Skyrme black holes.

Under the thin-shell approximation, we study the expansion of the shell formed around a single spherical void in the dust universe. We find that the peculiar velocity of the shell is determined mostly by the density parameter OMEGA0. It also depends on the interior dust energy density, but is not so sensitive to a cosmological constant. This feature may open a possibility of determining the universe model from the surface motion of voids.

Extending our recent proof of the cosmic no-hair theorem for Bianchi models in power-law inflation, we prove a more general cosmic no-hair theorem for all 0 less-than-or-equal-to lambda &lt; square-root 2, where lambda is the coupling constant of an exponential potential of an inflaton phi, exp(-lambdakappaphi). For any initially expanding Bianchi-type model except type IX, we find that the isotropic inflationary solution is the unique attractor and that anisotropies always enhance inflation. For Bianchi IX, this conclusion is also true, if the initial ratio of the vacuum energy LAMBDA(eff) to the maximum 3-curvature (3) R(max) is larger than 1/[3(1 - lambda2/2)] and its time derivative is initially positive. It turns out that the sufficient condition for inflation in Bianchi type-IX spacetimes with cosmological constant LAMBDA, which is a special case of the theorem (lambda = 0), becomes less restrictive than Wald's one. For type IX, we also show a recollapse theorem.

We investigate black holes in asymptotically de Sitter space-times. We show that a trapped surface always appears inside the event horizon and the total area of the black holes does not decrease as in asymptotically flat space-times. We find, however, that there is an upper bound on the area of apparent horizons in a wide class of asymptotically de Sitter space-times, in contrast with asymptotically flat space-times. This implies that black holes with a large area cannot collide with each other in asymptotically de Sitter space-time, unless a naked singularity is formed. On the basis of these results we argue that the inflationary scenario works even for initially inhomogeneous universes.

We present the analytic solution of N Einstein-Rosen bridges (''N black holes'') in the space-time with a cosmological constant LAMBDA and analyze it for one- and two-bridge systems. We discuss the three kinds of apparent horizons: i.e., the black-hole, white-hole, and cosmological apparent horizons. In the case of two Einstein-Rosen bridges, when the ''total mass'' is larger than a critical value, the black-hole apparent horizon surrounding two Einstein-Rosen bridges is not formed even if the distance is very short. Furthermore, in this case, the cosmological apparent horizon enclosing both bridges does not appear. Hence, it seems that when the ''total mass'' is very large, the Einstein-Rosen bridges cannot collapse into one black hole unless the ''gravitational mass'' is released in some way.

We investigate the initial data for localized gravitational waves in space-time with a cosmological constant LAMBDA. Using a conformal transformation, we find that the Hamiltonian and momentum constraints in the conformal frame turn out to be the same as those for a vacuum space-time without LAMBDA. As initial data, we consider Brill's waves in the conformal frame and discuss the trapped and antitrapped surfaces in the physical frame. Just as Brill's wave in asymptotically flat space-time, the gravitational ''mass'' of our case is positive; however, the waves with a large gravitational mass do not always provide trapped surfaces in contrast with the case of LAMBDA = 0. The large amount of gravitational waves, hence, does not seem to be an obstacle to the cosmic no-hair conjecture.

A Kerr-de Sitter black hole loses energy and angular momentum through both quantum superradiance and thermal emission. Our investigation of the former process indicates that a rapidly rotating black hole spins down faster as we increase LAMBDA, but after spinning down takes longer to evaporate.

We prove a cosmic no-hair theorem for Bianchi models in power-law inflation. Provided that the potential of an inflation phi is exp( -lambda-kappa-phi) with 0 less-than-or-equal-to lambda &lt; square-root 2/3, we find that the isotropic power-law solution is the unique attractor for any initially expanding Bianchi-type models except type IX. For Bianchi type IX, this conclusion is also true if the initial ratio of the vacuum energy to the maximum three-curvature is larger than one half.

We analyze the details of soft inflationary models, which have two scalar fields: one is the standard inflaton, whose potential is exponentially coupled to the other field. Such models are derived from both fundamental theories, and in the conformal frame of generalized Einstein theories. In the latter case, a nonstandard exponential coupling to the inflaton kinetic term also may arise. We list and discuss the various theories which give soft inflation, and then consider the satisfaction of the inflationary constraints in general models. We then specialize to new and chaotic inflation potentials, with both standard and nonstandard kinetic terms. The density perturbations are reduced sufficiently so that new inflation works well, with the coupling constant near the values allowed by grand unified theories. For chaotic inflation with a massive inflaton, we find successful inflation without any fine-tuning of the coupling constant or initial data.

Three-dimensional numerical relativity is applied to an investigation of the so-called "cosmic no-hair conjecture," which has been proposed to explain the homogeneity and isotropy of the present Universe via the inflationary scenario. We present a general formalism to study this cosmological problem using numerical relativity. Following this formalism, we find general solutions of the linearized Einstein equation in the de Sitter background and discuss a homogenization mechanism in the linear regime.

The particle creation effect on the higher-dimensional Kaluza-Klein cosmologies with M4×S7 topology is studied. This quantum effect is found to change the classical behavior of the internal and external scale factors drastically in the early stage of the expansion, so that the dimensional reduction seems to fail. However, at the later stage two scale factors get separated from each other and the internal scale factor approaches the final singularity just like the vacuum case. © 1984.